BTypes.jl

A model in openBF consists of a collection of vessels, a heart, and a description of blood mechanical properties. Vessels should be defined to be of type Vessel, the inlet boundary condition is of type Heart, and the blood properties are contained in a Blood instance.

 
module BTypes

Instances of BTypes data structures can be created as

BTypes.Vessel(args...)
BTypes.Heart(args...)
BTypes.Blood(args...)

where the args... are specified for each data structure in the following. Functions in initialise.jl generate instances of BTypes data structures.

 
export Vessel, Heart, Blood

Each vessel in the arterial system is represented by a single instance of type Vessel.

Arguments:
label Vessel clinical name. It is used in initialiseVessel to generate output file names.
ID Vessel ID within the Graph structure defined in main.jl. Unique integer.
sn Source node ID within the Graph structure. Unique integer.
tn Terminal node ID within the Graph structure. Unique integer.
M Number of nodes along the vessel. This is user defined in the project project_model.csv file.
dx \(\Delta x\) gives the spatial discretisation and it is computed once in initialise.jl.
Ccfl Courant-Friedrichs-Lewy (CFL) number. It is used to compute the \(\Delta t\) by calculateDeltaT at each time step. The CFL is always in the interval \([0,1]\).
beta Elastic constant used to compute the trans-mural pressure P.
gamma Elastic constant used by waveSpeed to compute c.
R0 Unstressed lumen radius.
A0 Unstressed cross-sectional area.
A Cross-sectional area at each node along the vessel.
Q Flow-rate at each node along the vessel.
u Axial velocity at each node along the vessel.
c Wave speed at each node along the vessel.
P Trans-mural pressure at each node along the vessel.
W1M0 Backward Riemann invariant at \(x=L\).
W2M0 Forward Riemann invariant.
U00A A in the ghost cell between 0 and -1. Ghost cells are used in godunov.jl to compute correctly the solution at boundaries cells.
U01A A in the ghost cell between -1 and -2.
UM1A A in the ghost cell between M and M+1.
UM2A A in the ghost cell between M+1 and M+2. Ghost cells are defined for Q in the same manner.
temp_P_name Name of temporary file where to store P values while running the solution. Temporary files (.temp) are created for all the variables (Q, A, u, c). Temporary files are handled by functions defined in IOutilities.jl.
out_P_name Name of final output file where to store P values. Every variable has its own .out file.
temp_P Julia handle to direct the output writing operation. Every variable has its own IOStream.
Rt Outlet reflection coefficient. See boundary_conditions.jl.
R1 Three element windkessel proximal resistance.
R2 Peripheral resistance.
Cc Peripheral compliance.
Pc Pressure through peripheral compliance. 

type Vessel
  label :: String

  #Topological notation
  ID :: Int64
  sn :: Int64
  tn :: Int64
  rn :: Int64

  #Numerical constants
  M       :: Int64
  dx      :: Float64
  invDx   :: Float64
  halfDx  :: Float64
  Ccfl    :: Float64

  #Physical constants
  beta  :: Array{Float64, 1}
  gamma :: Array{Float64, 1}
  gamma_ghost :: Array{Float64, 1}
  A0    :: Array{Float64, 1}
  dA0dx :: Array{Float64, 1}
  dTaudx :: Array{Float64, 1}
  Pext  :: Float64

  #Iterative solution
  A :: Array{Float64, 1}
  Q :: Array{Float64, 1}
  u :: Array{Float64, 1}
  c :: Array{Float64, 1}
  P :: Array{Float64, 1}

  #Riemann invariants
  W1M0 :: Float64
  W2M0 :: Float64

  #Ghost cells
  U00A :: Float64
  U00Q :: Float64
  U01A :: Float64
  U01Q :: Float64

  UM1A :: Float64
  UM1Q :: Float64
  UM2A :: Float64
  UM2Q :: Float64

  #Temporary files name
  temp_P_name :: String
  temp_Q_name :: String
  temp_A_name :: String
  temp_c_name :: String
  temp_u_name :: String

  last_P_name :: String
  last_Q_name :: String
  last_A_name :: String
  last_c_name :: String
  last_u_name :: String

  #Output files name
  out_P_name :: String
  out_Q_name :: String
  out_A_name :: String
  out_c_name :: String
  out_u_name :: String

  #Temporary files IOstreams
  temp_P :: IOStream
  temp_Q :: IOStream
  temp_A :: IOStream
  temp_c :: IOStream
  temp_u :: IOStream

  last_P :: IOStream
  last_Q :: IOStream
  last_A :: IOStream
  last_c :: IOStream
  last_u :: IOStream

  #Saving locations
  node2 :: Int64
  node3 :: Int64
  node4 :: Int64

  #Peripheral boundary condition
  Rt :: Float64

  R1 :: Float64
  R2 :: Float64
  Cc :: Float64
  Pc :: Float64

  #Slope
  slope :: Array{Float64, 1}

  #MUSCLArrays
  flux :: Array{Float64, 2}
  uStar :: Array{Float64, 2}

  vA :: Array{Float64, 1}
  vQ :: Array{Float64, 1}

  dU :: Array{Float64, 2}

  slopesA :: Array{Float64, 1}
  slopesQ :: Array{Float64, 1}

  Al :: Array{Float64, 1}
  Ar :: Array{Float64, 1}

  Ql :: Array{Float64, 1}
  Qr :: Array{Float64, 1}

  Fl :: Array{Float64, 2}
  Fr :: Array{Float64, 2}

end

The inlet boundary condition is applied to the first vessel in the model. A Heart instance contains all inlet information.

Arguments:
BC_switch Integer flag to select inlet boundary condition. It takes values from 1 to 4 and it is chosen by the user in the project_constants.jl file.
cardiac_T Cardiac period.
sys_T Length of systole.
initial_flow Q (ml/s) initial value to be set within all the vessels.
flow_amplitude Q maximum amplitude (ml/s) for the user-defined inlet boundary condition.
input_data Matrix defined as [time::Array, flow::Array] to be used as inlet boundary condition. 

type Heart
  BC_switch  :: Int64
  inlet_type :: String

  cardiac_T :: Float64
  sys_T     :: Float64

  initial_flow   :: Float64
  flow_amplitude :: Float64

  input_data :: Array{Float64, 2}
end

Blood mechanical properties.

Arguments :
mu Dynamic viscosity (poise)
rho Density (kg/m\(^3\))
Cf Viscous loss coefficient (see loadGlobalConstants and source). 

type Blood
  mu  :: Float64
  rho :: Float64
  Cf  :: Float64
  gamma_profile :: Float64
end



end